Problem: $ \left(\dfrac{1}{8}\right)^{-\frac{7}{3}}$
$= 8^{\frac{7}{3}}$ $= \left(8^{\frac{1}{3}}\right)^{7}$ To simplify $8^{\frac{1}{3}}$ , figure out what goes in the blank: $\left(? \right)^{3}=8$ To simplify $8^{\frac{1}{3}}$ , figure out what goes in the blank: $\left({2}\right)^{3}=8$ so $ 8^{\frac{1}{3}}=2$ So $8^{\frac{7}{3}}=\left(8^{\frac{1}{3}}\right)^{7}=2^{7}$ $= 2\cdot2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2$ $= 4\cdot2\cdot 2\cdot 2\cdot 2\cdot 2$ $= 8\cdot2\cdot 2\cdot 2\cdot 2$ $= 16\cdot2\cdot 2\cdot 2$ $= 32\cdot2\cdot 2$ $= 64\cdot2$ $= 128$